GAA - Grup d'Astronomia i Astrofísica
http://hdl.handle.net/2117/1136
2017-05-25T16:33:25ZA Parameterized multi-step Newton method for solving systems of nonlinear equations
http://hdl.handle.net/2117/104811
A Parameterized multi-step Newton method for solving systems of nonlinear equations
Ahmad, Fayyaz; Tohidi, Emran; Carrasco, Juan A.
We construct a novel multi-step iterative method for solving systems of nonlinear equations by introducing a parameter. to generalize the multi-step Newton method while keeping its order of convergence and computational cost. By an appropriate selection of theta, the new method can both have faster convergence and have larger radius of convergence. The new iterative method only requires one Jacobian inversion per iteration, and therefore, can be efficiently implemented using Krylov subspace methods. The new method can be used to solve nonlinear systems of partial differential equations, such as complex generalized Zakharov systems of partial differential equations, by transforming them into systems of nonlinear equations by discretizing approaches in both spatial and temporal independent variables such as, for instance, the Chebyshev pseudo-spectral discretizing method. Quite extensive tests show that the new method can have significantly faster convergence and significantly larger radius of convergence than the multi-step Newton method.
2017-05-24T10:09:04ZAhmad, FayyazTohidi, EmranCarrasco, Juan A.We construct a novel multi-step iterative method for solving systems of nonlinear equations by introducing a parameter. to generalize the multi-step Newton method while keeping its order of convergence and computational cost. By an appropriate selection of theta, the new method can both have faster convergence and have larger radius of convergence. The new iterative method only requires one Jacobian inversion per iteration, and therefore, can be efficiently implemented using Krylov subspace methods. The new method can be used to solve nonlinear systems of partial differential equations, such as complex generalized Zakharov systems of partial differential equations, by transforming them into systems of nonlinear equations by discretizing approaches in both spatial and temporal independent variables such as, for instance, the Chebyshev pseudo-spectral discretizing method. Quite extensive tests show that the new method can have significantly faster convergence and significantly larger radius of convergence than the multi-step Newton method.Multi-step frozen Jacobian iterative scheme for solving IVPs and BVPs based on higher order Fréchet derivatives
http://hdl.handle.net/2117/104772
Multi-step frozen Jacobian iterative scheme for solving IVPs and BVPs based on higher order Fréchet derivatives
Ilyas, Iqra; Ali, Zulqar; Ahmad, Fayyaz; Ullah, Malik Zaka; Alshomrani, Ali Saleh
A multi-step frozen Jacobian iterative scheme for solving system of nonlinear equations associated with IVPs (initial value problems) and BVPs (boundary value problems) is constructed. The multi-step iterative schemes consist of two parts, namely base method and a multi-step part. The proposed iterative scheme uses higher order Fr ´echet derivatives in the base method part and offers high convergence order (CO) 3s + 1, here s is the number of steps.
The increment in the CO per step is three, and we solve three upper and lower triangles systems per step in the multi-step part. A single inversion of the is not working in latexfrozen Jacobian is required and in fact, we avoid the direct inversion of the frozen Jacobian by computing the LU factors. The LU-factors are utilized in the multi-step part to solve upper and lower triangular systems repeatedly that makes the iterative scheme computationally efficient. We solve a set of IVPs and BVPs to show the validity, accuracy and efficiency of our proposed iterative scheme.
2017-05-23T11:55:56ZIlyas, IqraAli, ZulqarAhmad, FayyazUllah, Malik ZakaAlshomrani, Ali SalehA multi-step frozen Jacobian iterative scheme for solving system of nonlinear equations associated with IVPs (initial value problems) and BVPs (boundary value problems) is constructed. The multi-step iterative schemes consist of two parts, namely base method and a multi-step part. The proposed iterative scheme uses higher order Fr ´echet derivatives in the base method part and offers high convergence order (CO) 3s + 1, here s is the number of steps.
The increment in the CO per step is three, and we solve three upper and lower triangles systems per step in the multi-step part. A single inversion of the is not working in latexfrozen Jacobian is required and in fact, we avoid the direct inversion of the frozen Jacobian by computing the LU factors. The LU-factors are utilized in the multi-step part to solve upper and lower triangular systems repeatedly that makes the iterative scheme computationally efficient. We solve a set of IVPs and BVPs to show the validity, accuracy and efficiency of our proposed iterative scheme.Orbital periods and component masses of three double white dwarfs
http://hdl.handle.net/2117/104493
Orbital periods and component masses of three double white dwarfs
Rebassa Mansergas, Alberto; Parsons, S. G.; García-Berro Montilla, Enrique; Gaensicke, B. T.; Schreiber, Mathias R.; Rybicka, M.; Koester, D.
The merger of close double white dwarfs (CDWDs) is one of the favourite evolutionary channels for producing Type Ia supernovae (SN Ia). Unfortunately, current theories of the evolution and formation of CDWDs are still poorly constrained and have several serious uncertainties that affect the predicted SN Ia rates. Moreover, current observational constraints on this evolutionary pathway for SN Ia mainly rely on only 17 double-lined and/or eclipsing CDWDs with measured orbital and stellar parameters for both white dwarfs. In this paper, we present the orbital periods and the individual masses of three new double-lined CDWDs, derived using a new method. This method employs mass ratios, the Ha core ratios and spectral model fitting to constrain the masses of the components of the pair. The three CDWDs are WD0028-474 (P-orb = 9.350 +/- 0.007 h, M-1 = 0.60 +/- 0.06 M-circle dot, M-2 = 0.45 +/- 0.04 M-circle dot), HE0410-1137 (P-orb = 12.208 +/- 0.008 h, M-1 = 0.51 +/- 0.04 M-circle dot, M-2 = 0.39 +/- 0.03 M-circle dot) and SDSSJ031813.25-010711.7 (P-orb = 45.908 +/- 0.006 h, among the longest period systems, M-1 = 0.40 +/- 0.05 M-circle dot, M-2 = 0.49 +/- 0.05 M-circle dot). While the three systems studied here will merge in time-scales longer than the Hubble time and are expected to become single massive (greater than or similar to 0.9 M-circle dot) white dwarfs rather than exploding as SN Ia, increasing the small sample of CDWDs with determined stellar parameters is crucial for a better overall understanding of their evolution.
2017-05-16T10:37:49ZRebassa Mansergas, AlbertoParsons, S. G.García-Berro Montilla, EnriqueGaensicke, B. T.Schreiber, Mathias R.Rybicka, M.Koester, D.The merger of close double white dwarfs (CDWDs) is one of the favourite evolutionary channels for producing Type Ia supernovae (SN Ia). Unfortunately, current theories of the evolution and formation of CDWDs are still poorly constrained and have several serious uncertainties that affect the predicted SN Ia rates. Moreover, current observational constraints on this evolutionary pathway for SN Ia mainly rely on only 17 double-lined and/or eclipsing CDWDs with measured orbital and stellar parameters for both white dwarfs. In this paper, we present the orbital periods and the individual masses of three new double-lined CDWDs, derived using a new method. This method employs mass ratios, the Ha core ratios and spectral model fitting to constrain the masses of the components of the pair. The three CDWDs are WD0028-474 (P-orb = 9.350 +/- 0.007 h, M-1 = 0.60 +/- 0.06 M-circle dot, M-2 = 0.45 +/- 0.04 M-circle dot), HE0410-1137 (P-orb = 12.208 +/- 0.008 h, M-1 = 0.51 +/- 0.04 M-circle dot, M-2 = 0.39 +/- 0.03 M-circle dot) and SDSSJ031813.25-010711.7 (P-orb = 45.908 +/- 0.006 h, among the longest period systems, M-1 = 0.40 +/- 0.05 M-circle dot, M-2 = 0.49 +/- 0.05 M-circle dot). While the three systems studied here will merge in time-scales longer than the Hubble time and are expected to become single massive (greater than or similar to 0.9 M-circle dot) white dwarfs rather than exploding as SN Ia, increasing the small sample of CDWDs with determined stellar parameters is crucial for a better overall understanding of their evolution.A preconditioned iterative method for solving systems of nonlinear equations having unknown multiplicity
http://hdl.handle.net/2117/104328
A preconditioned iterative method for solving systems of nonlinear equations having unknown multiplicity
Ahmad, Fayyaz; Bhutta, Toseef Akhter ; Sohaib, Umar; Ullah, Malik Zaka; Alshomrani, Ali Saleh; Ahmad, Shamshad; Ahmad, Shahid
A modification to an existing iterative method for computing zeros with unknown multiplicities of nonlinear equations or a system of nonlinear equations is presented. We introduce preconditioners to nonlinear equations or a system of nonlinear equations and their corresponding Jacobians. The inclusion of preconditioners provides numerical stability and accuracy. The different selection of preconditioner offers a family of iterative methods. We modified an existing method in a way that we do not alter its inherited quadratic convergence. Numerical simulations confirm the quadratic convergence of the preconditioned iterative method. The influence of preconditioners is clearly reflected in the numerically achieved accuracy of computed solutions.
2017-05-11T15:43:34ZAhmad, FayyazBhutta, Toseef Akhter Sohaib, UmarUllah, Malik ZakaAlshomrani, Ali SalehAhmad, ShamshadAhmad, ShahidA modification to an existing iterative method for computing zeros with unknown multiplicities of nonlinear equations or a system of nonlinear equations is presented. We introduce preconditioners to nonlinear equations or a system of nonlinear equations and their corresponding Jacobians. The inclusion of preconditioners provides numerical stability and accuracy. The different selection of preconditioner offers a family of iterative methods. We modified an existing method in a way that we do not alter its inherited quadratic convergence. Numerical simulations confirm the quadratic convergence of the preconditioned iterative method. The influence of preconditioners is clearly reflected in the numerically achieved accuracy of computed solutions.Non-extensive statistics to the cosmological lithium problem
http://hdl.handle.net/2117/104261
Non-extensive statistics to the cosmological lithium problem
Hou, S.Q.; He, J.J.; Parikh, Anuj Ramesh
Big Bang nucleosynthesis (BBN) theory predicts the abundances of the light elements D, 3He, 4He, and 7Li produced in the early universe. The primordial abundances of D and 4He inferred from observational data are in good agreement with predictions, however, BBN theory overestimates the primordial 7Li abundance by about a factor of three. This is the so-called
2017-05-10T11:04:38ZHou, S.Q.He, J.J.Parikh, Anuj RameshBig Bang nucleosynthesis (BBN) theory predicts the abundances of the light elements D, 3He, 4He, and 7Li produced in the early universe. The primordial abundances of D and 4He inferred from observational data are in good agreement with predictions, however, BBN theory overestimates the primordial 7Li abundance by about a factor of three. This is the so-calledMagnetic white dwarfs: Observations, theory and future prospects
http://hdl.handle.net/2117/104215
Magnetic white dwarfs: Observations, theory and future prospects
García-Berro Montilla, Enrique; Kilic, Mukremin; Kepler, S.O.
Isolated magnetic white dwarfs have field strengths ranging from 10(3)G to 10(9) G, and constitute an interesting class of objects. The origin of the magnetic field is still the subject of a hot debate. Whether these fields are fossil, hence the remnants of original weak magnetic fields amplified during the course of the evolution of the progenitor of white dwarfs, or on the contrary, are the result of binary interactions or, finally, other physical mechanisms that could produce such large magnetic fields during the evolution of the white dwarf itself, remains to be elucidated. In this work, we review the current status and paradigms of magnetic fields in white dwarfs, from both the theoretical and observational points of view.
2017-05-09T07:37:09ZGarcía-Berro Montilla, EnriqueKilic, MukreminKepler, S.O.Isolated magnetic white dwarfs have field strengths ranging from 10(3)G to 10(9) G, and constitute an interesting class of objects. The origin of the magnetic field is still the subject of a hot debate. Whether these fields are fossil, hence the remnants of original weak magnetic fields amplified during the course of the evolution of the progenitor of white dwarfs, or on the contrary, are the result of binary interactions or, finally, other physical mechanisms that could produce such large magnetic fields during the evolution of the white dwarf itself, remains to be elucidated. In this work, we review the current status and paradigms of magnetic fields in white dwarfs, from both the theoretical and observational points of view.A common origin of magnetism from planets to white dwarfs
http://hdl.handle.net/2117/104213
A common origin of magnetism from planets to white dwarfs
Isern Vilaboy, Jordi; García-Berro Montilla, Enrique; Kulebi, Baybar; Loren Aguilar, Pablo
Isolated magnetic white dwarfs have field strengths ranging from kilogauss to gigagauss. However, the origin of the magnetic field has not been hitherto elucidated. Whether these fields are fossil, hence the remnants of original weak magnetic fields amplified during the course of the evolution of their progenitor stars, or are the result of binary interactions, or, finally, they are produced by other internal physical mechanisms during the cooling of the white dwarf itself, remains a mystery. At sufficiently low temperatures, white dwarfs crystallize. Upon solidification, phase separation of its main constituents, 12C and 16O, and of the impurities left by previous evolution occurs. This process leads to the formation of a Rayleigh–Taylor unstable liquid mantle on top of a solid core. This convective region, as it occurs in solar system planets like the Earth and Jupiter, can produce a dynamo able to yield magnetic fields of strengths of up to 0.1 MG, thus providing a mechanism that could explain magnetism in single white dwarfs.
2017-05-09T07:28:26ZIsern Vilaboy, JordiGarcía-Berro Montilla, EnriqueKulebi, BaybarLoren Aguilar, PabloIsolated magnetic white dwarfs have field strengths ranging from kilogauss to gigagauss. However, the origin of the magnetic field has not been hitherto elucidated. Whether these fields are fossil, hence the remnants of original weak magnetic fields amplified during the course of the evolution of their progenitor stars, or are the result of binary interactions, or, finally, they are produced by other internal physical mechanisms during the cooling of the white dwarf itself, remains a mystery. At sufficiently low temperatures, white dwarfs crystallize. Upon solidification, phase separation of its main constituents, 12C and 16O, and of the impurities left by previous evolution occurs. This process leads to the formation of a Rayleigh–Taylor unstable liquid mantle on top of a solid core. This convective region, as it occurs in solar system planets like the Earth and Jupiter, can produce a dynamo able to yield magnetic fields of strengths of up to 0.1 MG, thus providing a mechanism that could explain magnetism in single white dwarfs.The SDSS spectroscopic catalogue of white dwarf-main-sequence binaries: new identifications from DR 9–12
http://hdl.handle.net/2117/104211
The SDSS spectroscopic catalogue of white dwarf-main-sequence binaries: new identifications from DR 9–12
Rebassa Mansergas, Alberto; Ren, J. J.; Parsons, S. G.; Gänsicke, Boris T.; Schreiber, Mathias R.; García-Berro Montilla, Enrique; Liu, X.; Koester, D.
We present an updated version of the spectroscopic catalogue of white dwarf-main-sequence (WDMS) binaries from the Sloan Digital Sky Survey (SDSS). We identify 938 WDMS binaries within the data releases (DR) 9-12 of SDSS plus 40 objects from DR 1-8 that we missed in our previous works, 646 of which are new. The total number of spectroscopic SDSS WDMS binaries increases to 3294. This is by far the largest and most homogeneous sample of compact binaries currently available. We use a decomposition/fitting routine to derive the stellar parameters of all systems identified here (white dwarf effective temperatures, surface gravities and masses, and secondary star spectral types). The analysis of the corresponding stellar parameter distributions shows that the SDSS WDMS binary population is seriously affected by selection effects. We also measure the NaI lambda lambda 8183.27, 8194.81 absorption doublet and H alpha emission radial velocities (RV) from all SDSS WDMS binary spectra identified in this work. 98 objects are found to display RV variations, 62 of which are new. The RV data are sufficient enough to estimate the orbital periods of three close binaries.
2017-05-09T06:59:02ZRebassa Mansergas, AlbertoRen, J. J.Parsons, S. G.Gänsicke, Boris T.Schreiber, Mathias R.García-Berro Montilla, EnriqueLiu, X.Koester, D.We present an updated version of the spectroscopic catalogue of white dwarf-main-sequence (WDMS) binaries from the Sloan Digital Sky Survey (SDSS). We identify 938 WDMS binaries within the data releases (DR) 9-12 of SDSS plus 40 objects from DR 1-8 that we missed in our previous works, 646 of which are new. The total number of spectroscopic SDSS WDMS binaries increases to 3294. This is by far the largest and most homogeneous sample of compact binaries currently available. We use a decomposition/fitting routine to derive the stellar parameters of all systems identified here (white dwarf effective temperatures, surface gravities and masses, and secondary star spectral types). The analysis of the corresponding stellar parameter distributions shows that the SDSS WDMS binary population is seriously affected by selection effects. We also measure the NaI lambda lambda 8183.27, 8194.81 absorption doublet and H alpha emission radial velocities (RV) from all SDSS WDMS binary spectra identified in this work. 98 objects are found to display RV variations, 62 of which are new. The RV data are sufficient enough to estimate the orbital periods of three close binaries.An asteroseismic constraint on the mass of the axion from the period drift of the pulsating da white dwarf star L19-2
http://hdl.handle.net/2117/104210
An asteroseismic constraint on the mass of the axion from the period drift of the pulsating da white dwarf star L19-2
Córsico, Alejandro H.; Romero, Alejandra Daniela; Althaus, Leandro G.; García-Berro Montilla, Enrique; Isern Vilaboy, Jordi; Kepler, S.O.; Miller Bartolami, Marcelo M.; Sullivan, Denis J.
We employ an asteroseismic model of L19-2, a relatively massive (Msstarf ~ 0.75 M¿) and hot (Teff ~ 12 100 K) pulsating DA (H-rich atmosphere) white dwarf star (DAV or ZZ Ceti variable), and use the observed values of the temporal rates of period change of its dominant pulsation modes (¿ ~ 113 s and ¿ ~ 192 s), to derive a new constraint on the mass of the axion, the hypothetical non-barionic particle considered as a possible component of the dark matter of the Universe. If the asteroseismic model employed is an accurate representation of L19-2, then our results indicate hints of extra cooling in this star, compatible with emission of axions of mass ma cos2ß lesssim 25 meV or an axion-electron coupling constant of gae lesssim 7 × 10-13.
2017-05-09T06:38:11ZCórsico, Alejandro H.Romero, Alejandra DanielaAlthaus, Leandro G.García-Berro Montilla, EnriqueIsern Vilaboy, JordiKepler, S.O.Miller Bartolami, Marcelo M.Sullivan, Denis J.We employ an asteroseismic model of L19-2, a relatively massive (Msstarf ~ 0.75 M¿) and hot (Teff ~ 12 100 K) pulsating DA (H-rich atmosphere) white dwarf star (DAV or ZZ Ceti variable), and use the observed values of the temporal rates of period change of its dominant pulsation modes (¿ ~ 113 s and ¿ ~ 192 s), to derive a new constraint on the mass of the axion, the hypothetical non-barionic particle considered as a possible component of the dark matter of the Universe. If the asteroseismic model employed is an accurate representation of L19-2, then our results indicate hints of extra cooling in this star, compatible with emission of axions of mass ma cos2ß lesssim 25 meV or an axion-electron coupling constant of gae lesssim 7 × 10-13.A higher order frozen Jacobian iterative method for solving Hamilton-Jacobi equations
http://hdl.handle.net/2117/103758
A higher order frozen Jacobian iterative method for solving Hamilton-Jacobi equations
Alzahrani, Ebraheem O.; Alaidarous, Eman; Younas, Arshad M. M.; Ahmad, Fayyaz; Ahmad, Shamshad; Ahmad, Shahid
It is well-known that the solution of Hamilton-Jacobi equation may have singularity i.e., the solution is non-smooth or nearly non-smooth. We construct a frozen Jacobian multi-step iterative method for solving Hamilton-Jacobi equation under the assumption that the solution is nearly singular. The frozen Jacobian iterative methods are computationally very efficient because a single instance of the iterative method uses a single inversion (in the scene of LU factorization) of the frozen Jacobian. The multi-step part enhances the convergence order by solving lower and upper triangular systems. The convergence order of our proposed iterative method is 3(m-1) for m>=3. For attaining good numerical accuracy in the solution, we use Chebyshev pseudo-spectral collocation method. Some Hamilton-Jacobi equations are solved, and numerically obtained results show high accuracy.
2017-04-26T14:48:38ZAlzahrani, Ebraheem O.Alaidarous, EmanYounas, Arshad M. M.Ahmad, FayyazAhmad, ShamshadAhmad, ShahidIt is well-known that the solution of Hamilton-Jacobi equation may have singularity i.e., the solution is non-smooth or nearly non-smooth. We construct a frozen Jacobian multi-step iterative method for solving Hamilton-Jacobi equation under the assumption that the solution is nearly singular. The frozen Jacobian iterative methods are computationally very efficient because a single instance of the iterative method uses a single inversion (in the scene of LU factorization) of the frozen Jacobian. The multi-step part enhances the convergence order by solving lower and upper triangular systems. The convergence order of our proposed iterative method is 3(m-1) for m>=3. For attaining good numerical accuracy in the solution, we use Chebyshev pseudo-spectral collocation method. Some Hamilton-Jacobi equations are solved, and numerically obtained results show high accuracy.